Spontaneous Breaking of N = 2 to N = 1 in Supergravity

Abstract

We address some issues related to spontaneous N = 2 ! N = 1 supersymmetry breaking in supergravity. In particular, we discuss the super-Higgs eect in N = 2 supergravity and give the general conditions for the scalar potential which preserves N = 1 supersymmetry with various ground states of the scalar potential such as the Minkowski ground states and the spaces of constant curvature (anti-de Sitter). Furthermore, we also derive the low energy eective N = 1 theory by integrating out the massive gravitino multiplet and show that it saties non-trivial consistency conditions which can also be viewed as conditions on the geometry of the scalar manifold. 
As an example we brie y discuss the scalar manifold SU(1;1)/U(1) x SO(4;1)/SO(4)